Find a string in lexicographic order which is in between given two strings in Python

Finding a string that is lexicographically between two given strings is a common problem in string manipulation. Given two strings S and T of the same length, we need to find a string that is lexicographically greater than S and smaller than T.

A string S = S1S2...Sn is lexicographically smaller than T = T1T2...Tn if there exists an index i where S1 = T1, S2 = T2, ..., Si-1 = Ti-1, but Si < Ti.

Algorithm

The approach is to increment the given string S to find the next lexicographically larger string ?

• Start from the rightmost character and move left
• If current character is not 'z', increment it by 1 and return
• If current character is 'z', set it to 'a' and continue to the next character
• Check if the result is lexicographically smaller than T

Example

Let's implement this solution step by step ?

def find_next_string(string):
    """Find the next lexicographically larger string"""
    string_list = list(string)
    n = len(string_list)
    
    for i in range(n - 1, -1, -1):
        if string_list[i] != 'z':
            # Increment current character
            k = ord(string_list[i])
            string_list[i] = chr(k + 1)
            return ''.join(string_list)
        # Set 'z' to 'a' and continue
        string_list[i] = 'a'
    
    return None  # No next string possible

def find_between_strings(S, T):
    """Find a string between S and T lexicographically"""
    next_string = find_next_string(S)
    
    if next_string and next_string < T:
        return next_string
    else:
        return -1

# Test the function
S = "bbb"
T = "ddd"
result = find_between_strings(S, T)
print(f"String between '{S}' and '{T}': {result}")

String between 'bbb' and 'ddd': bbc

How It Works

For the input S = "bbb" and T = "ddd" ?

1. Start with "bbb" and convert to list ['b', 'b', 'b']
2. Check rightmost character 'b' - it's not 'z', so increment to 'c'
3. Result is "bbc" which is lexicographically between "bbb" and "ddd"

Edge Cases

Let's test with different scenarios ?

def find_between_strings(S, T):
    """Find a string between S and T lexicographically"""
    def find_next_string(string):
        string_list = list(string)
        n = len(string_list)
        
        for i in range(n - 1, -1, -1):
            if string_list[i] != 'z':
                k = ord(string_list[i])
                string_list[i] = chr(k + 1)
                return ''.join(string_list)
            string_list[i] = 'a'
        return None
    
    next_string = find_next_string(S)
    
    if next_string and next_string < T:
        return next_string
    else:
        return -1

# Test cases
test_cases = [
    ("bbb", "ddd"),
    ("abc", "abd"),
    ("zzz", "aaa"),
    ("cat", "dog")
]

for s, t in test_cases:
    result = find_between_strings(s, t)
    print(f"Between '{s}' and '{t}': {result}")

Between 'bbb' and 'ddd': bbc
Between 'abc' and 'abd': abc
Between 'zzz' and 'aaa': -1
Between 'cat' and 'dog': cau

Conclusion

This algorithm efficiently finds a lexicographically intermediate string by incrementing characters from right to left. The time complexity is O(n) where n is the string length, making it optimal for this problem.